Radically coupled resins and methods of making and using same

ABSTRACT

An ethylene polymer having a density greater than about 0.930 g/ml and a level of long chain branching ranging from about 0.001 LCB/10 3  carbons to about 1.5 LCB/10 3  carbons as determined by SEC-MALS. An ethylene polymer having a level of short chain branching ranging from about 0 to about 10 mol. % and a level of long chain branching ranging from about 0.001 LCB/10 3  carbons to about 1.5 LCB/10 3  carbons as determined by SEC-MALS. An ethylene polymer having a polydispersity index ranging from about 8 to about 25 and a level of long chain branching ranging from about 0.001 LCB/10 3  carbons to about 1.5 LCB/10 3  carbons as determined by SEC-MALS.

TECHNICAL FIELD

The present disclosure relates to novel polymers and methods of makingand using same. More specifically, the present disclosure relates topolymers having improved process ability.

BACKGROUND

Polymers, such as polyethylene homopolymers and copolymers, are used forthe production of a wide variety of articles. The use of a particularpolymer in a particular application will depend on the type of physicaland/or mechanical properties displayed by the polymer. Thus, there is anongoing need to develop polymers that display novel physical and/ormechanical properties and methods for producing these polymers.

BRIEF SUMMARY

Disclosed herein is an ethylene polymer having a density greater thanabout 0.930 g/ml and a level of long chain branching ranging from about0.001 LCB/10³ carbons to about 1.5 LCB/10³ carbons as determined bySEC-MALS.

Also disclosed herein is an ethylene polymer having a level of shortchain branching ranging from about 0 to about 10 mol. % and a level oflong chain branching ranging from about 0.001 LCB/10³ carbons to about1.5 LCB/10³ carbons as determined by SEC-MALS.

Also disclosed herein is an ethylene polymer having a polydispersityindex ranging from about 8 to about 25 and a level of long chainbranching ranging from about 0.001 LCB/10³ carbons to about 1.5 LCB/10³carbons as determined by SEC-MALS.

Also disclosed herein is an ethylene polymer having a density less thanabout 0.95 g/ml; a length of short chain branching wherein less thanabout 10% of the short-chain branches are odd; and a level of long chainbranching ranging from about 0.001 LCB/10³ carbons to about 1.5 LCB/10³carbons as determined by SEC-MALS.

Also disclosed herein is an ethylene polymer having a level of shortchain branching ranging from about 0 to about 10 mol. %; a length ofshort chain branching wherein less than about 10% of the short-chainbranches are odd; and a level of long chain branching ranging from about0.001 LCB/103 carbons to about 1.5 LCB/103 carbons as determined bySEC-MALS.

Also disclosed herein is an ethylene polymer having a density of greaterthan about 0.930 g/ml; an activation energy of from about 37 kJ mol⁻¹ toabout 55 kJ mol⁻¹; and a level of long chain branching ranging fromabout 0.001 LCB/10³ carbons to about 1.5 LCB/10³ carbons as determinedby SEC-MALS.

Also disclosed herein is an ethylene polymer having a level of shortchain branching ranging from about 0 to about 10 mol. %; an activationenergy of from about 37 kJ mol⁻¹ to about 55 kJ mol⁻¹; and a level oflong chain branching ranging from about 0.001 LCB/10³ carbons to about1.5 LCB/10³ carbons as determined by SEC-MALS.

Also disclosed herein is an ethylene polymer having a density greaterthan about 0.930 g/ml; and a level of long chain branching ranging fromabout 0.001 LCB/10³ carbons to about 1.5 LCB/10³ carbons as determinedby SEC-MALS wherein for a weight-average molecular weight ranging fromabout 25 kDa to about 175 kDa, a value of Eta₀ is less than y wherey=2E09x²−1E+12x+6E13 and x is the weight-average molecular weight.

Also disclosed herein is an ethylene polymer having a level of shortchain branching ranging from about 0 to about 10 mol. %; and a level oflong chain branching ranging from about 0.001 LCB/10³ carbons to about1.5 LCB/10³ carbons as determined by SEC-MALS wherein for a weightaverage molecular weight ranging from about 25 kDa to about 175 kDa, avalue of Eta₀ is less than y where y=2E09x²−1E+12x+6E13 and x is theweight-average molecular weight.

Also disclosed herein is an ethylene polymer having a level of shortchain branching ranging from about 0 to about 10 mol. %; and a level oflong chain branching ranging from about 0.001 LCB/10³ carbons to about1.5 LCB/10³ carbons as determined by SEC-MALS wherein for a weightaverage molecular weight ranging from about 25 kDa to about 175 kDa, avalue of Eta₀ is less than y where y=2E09x²−1E+12x+6E13 and x is theweight-average molecular weight.

Also disclosed herein is a method comprising melt extruding a wax havinga weight-average molecular weight ranging from about 50 kDa to about 350kDa in the presence of at least one coupling compound and an optionalcoagent wherein the coupling agent is a free radical initiator andrecovering a radically coupled resin.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot of the molecular weight distribution profile forsamples from Example 3.

FIG. 2 is a plot of the variation of the melt index and high load meltindex with peroxide loading for the samples from Example 3.

FIG. 3 is the SEC-MALS analysis of the samples from Example 3.

FIG. 4 is a plot of the dynamic melt viscosity of the samples fromExample 3

FIG. 5 is a plot of the dynamic melt viscosity vs. frequency of thesamples from Example 3.

FIG. 6 is a comparison of the molecular weight of a sample from Example3 with commercial LDPE resins.

FIG. 7 is a comparison of the dynamic melt viscosity of a sample fromExample 3 with commercial LDPE resins.

FIG. 8 is a comparison of the plot of zero-shear viscosity as a functionof weight average molecular weight of a sample from Example 3 andcommercial LDPE resins.

FIG. 9 is a plot of the molecular weight distribution profile of samplesfrom Example 4.

FIG. 10 is a plot of the variation of the melt index and high load meltindex with peroxide loading of samples from Example 4.

FIG. 11 is a plot of the dynamic melt viscosity of samples from Example3

FIG. 12 is a plot of the dynamic melt viscosity vs. frequency of samplesfrom Example 4.

FIG. 13 is a plot of the molecular weight distribution profile ofsamples from Example 5.

FIG. 14 is a plot of the variation of the melt index with peroxideloading for the samples from Example 5.

FIG. 15 is a plot of the dynamic melt viscosity of samples from Example5.

FIG. 16 is the SEC-MALS analysis of samples from Example 5.

FIG. 17 is a comparison of the weight average molecular weight ofsamples from Example 5 and commercial LDPE samples.

FIG. 18 is a comparison of dynamic melt rheology of samples from Example5 and commercial LDPE samples.

FIG. 19 is a plot of weight average molecular weight and zero-shearviscosity comparing samples from Example 5 with commercial LDPE samples.

DETAILED DESCRIPTION

Disclosed herein are polymers, polymer compositions and methods ofmaking and using same. In an embodiment, a method of the presentdisclosure comprises reactive extrusion of a parent polymer (PARPOL) toproduce a radically coupled resin (RCR). In an embodiment, the RCRexhibits a polymer architecture characterized by an elevated frequencyof topological variations resulting in a polymer having improvedrheological characteristics and processability over a broad range ofdensities. In an embodiment, the topological variations comprise longchain branching. Polymers of the type disclosed herein (i.e., RCR) maybe characterized by a polymer architecture that results in rheologicalcharacteristics of the type disclosed herein.

To define more clearly the terms used herein, the following definitionsare provided. Unless otherwise indicated, the following definitions areapplicable to this disclosure. If a term is used in this disclosure butis not specifically defined herein, the definition from the IUPACCompendium of Chemical Terminology, 2^(nd) Ed (1997) can be applied, aslong as that definition does not conflict with any other disclosure ordefinition applied herein, or render indefinite or non-enabled any claimto which that definition is applied. To the extent that any definitionor usage provided by any document incorporated herein by referenceconflicts with the definition or usage provided herein, the definitionor usage provided herein controls.

Groups of elements of the table are indicated using the numbering schemeindicated in the version of the periodic table of elements published inChemical and Engineering News, 63(5), 27, 1985. In some instances agroup of elements may be indicated using a common name assigned to thegroup; for example alkali earth metals (or alkali metals) for Group 1elements, alkaline earth metals (or alkaline metals) for Group 2elements, transition metals for Group 3-12 elements, and halogens forGroup 17 elements.

A chemical “group” is described according to how that group is formallyderived from a reference or “parent” compound, for example, by thenumber of hydrogen atoms formally removed from the parent compound togenerate the group, even if that group is not literally synthesized inthis manner. These groups can be utilized as substituents or coordinatedor bonded to metal atoms. By way of example, an “alkyl group” formallycan be derived by removing one hydrogen atom from an alkane, while an“alkylene group” formally can be derived by removing two hydrogen atomsfrom an alkane. Moreover, a more general term can be used to encompass avariety of groups that formally are derived by removing any number (“oneor more”) hydrogen atoms from a parent compound, which in this examplecan be described as an “alkane group,” and which encompasses an “alkylgroup,” an “alkylene group,” and materials have three or more hydrogenatoms, as necessary for the situation, removed from the alkane.Throughout, the disclosure that a substituent, ligand, or other chemicalmoiety may constitute a particular “group” implies that the well-knownrules of chemical structure and bonding are followed when that group isemployed as described. When describing a group as being “derived by,”“derived from,” “formed by,” or “formed from,” such terms are used in aformal sense and are not intended to reflect any specific syntheticmethods or procedure, unless specified otherwise or the context requiresotherwise.

The term “substituted” when used to describe a group, for example, whenreferring to a substituted analog of a particular group, is intended todescribe any non-hydrogen moiety that formally replaces a hydrogen atomin that group, and is intended to be non-limiting. A group or groups mayalso be referred to herein as “unsubstituted” or by equivalent termssuch as “non-substituted,” which refers to the original group in which anon-hydrogen moiety does not replace a hydrogen atom within that group.“Substituted” is intended to be non-limiting and include inorganicsubstituents or organic substituents.

Unless otherwise specified, any carbon-containing group for which thenumber of carbon atoms is not specified can have, according to properchemical practice, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, or 30 carbonatoms, or any range or combination of ranges between these values. Forexample, unless otherwise specified, any carbon-containing group canhave from 1 to 30 carbon atoms, from 1 to 25 carbon atoms, from 1 to 20carbon atoms, from 1 to 15 carbon atoms, from 1 to 10 carbon atoms, orfrom 1 to 5 carbon atoms, and the like. Moreover, other identifiers orqualifying terms may be utilized to indicate the presence or absence ofa particular substituent, a particular regiochemistry and/orstereochemistry, or the presence or absence of a branched underlyingstructure or backbone.

Within this disclosure the normal rules of organic nomenclature willprevail. For instance, when referencing substituted compounds or groups,references to substitution patterns are taken to indicate that theindicated group(s) is (are) located at the indicated position and thatall other non-indicated positions are hydrogen. For example, referenceto a 4-substituted phenyl group indicates that there is a non-hydrogensubstituent located at the 4 position and hydrogen atoms located at the2, 3, 5, and 6 positions. By way of another example, reference to a3-substituted naphth-2-yl indicates that there is a non-hydrogensubstituent located at the 3 position and hydrogen atoms located at the1, 4, 5, 6, 7, and 8 positions. References to compounds or groups havingsubstitutions at positions in addition to the indicated position will bereference using comprising or some other alternative language. Forexample, a reference to a phenyl group comprising a substituent at the 4position refers to a group having a non-hydrogen atom at the 4 positionand hydrogen or any non-hydrogen group at the 2, 3, 5, and 6 positions.

Embodiments disclosed herein the may provide the materials listed assuitable for satisfying a particular feature of the embodiment delimitedby the term “or.” For example, a particular feature of the disclosedsubject matter may be disclosed as follows: Feature X can be A, B, or C.It is also contemplated that for each feature the statement can also bephrased as a listing of alternatives such that the statement “Feature Xis A, alternatively B, or alternatively C” is also an embodiment of thepresent disclosure whether or not the statement is explicitly recited.

In an embodiment, the polymers disclosed herein are olefin oralpha-olefin polymers. Herein, the polymer refers both to a materialcollected as the product of a polymerization reaction (e.g., a reactoror virgin resin) and a polymeric composition comprising a polymer andone or more additives. In an embodiment, a monomer (e.g., ethylene) maybe polymerized using the methodologies disclosed herein to produce apolymer of the type disclosed herein. The polymer may comprise ahomopolymer. It is to be understood that an inconsequential amount ofcomonomer may be present in the polymers disclosed herein and thepolymer still be considered a homopolymer. Herein an inconsequentialamount of a comonomer refers to an amount that does not substantivelyaffect the properties of the polymer disclosed herein. For example acomonomer can be present in an amount of less than about 1.0 wt. %, 0.5wt. %, 0.1 wt. %, or 0.01 wt. % based on the total weight of polymer.

In an alternative embodiment, the polymer is a copolymer. Examples ofsuitable comonomers include without limitation unsaturated hydrocarbonshaving from 3 to 20 carbon atoms such as propylene, 1-butene, 1-pentene,1-hexene, 3-methyl-1-butene, 4-methyl-1-pentene, 1-heptene, 1-octene,1-nonene, 1-decene, and mixtures thereof. In an embodiment, the PARPOLis a polymer of ethylene, e.g., polyethylene (PE). The applicability ofthe aspects and features disclosed herein to linear olefin polymers(e.g., ethylene, propylene and 1-butylene) and olefin copolymers arealso contemplated. PARPOLs may be used for forming the novel polymers(e.g., radically coupled resins) of this disclosure.

In an embodiment, a PARPOL of the type described herein may be preparedby any suitable methodology, for example by employing one or morecatalyst systems, in one or more reactors, in solution, in slurry, or inthe gas phase, and/or by varying the monomer concentration in thepolymerization reaction, and/or by changing any/all of the materials orparameters involved in the production of the PARPOLs, as will bedescribed in more detail later herein.

The PARPOL of the present disclosure can be produced using various typesof polymerization reactors. As used herein, “polymerization reactor”includes any reactor capable of polymerizing olefin monomers to producehomopolymers and/or copolymers. Homopolymers and/or copolymers producedin the reactor may be referred to as resin and/or polymers. The varioustypes of reactors include, but are not limited to those that may bereferred to as batch, slurry, gas-phase, solution, high pressure,tubular, autoclave, or other reactor and/or reactors. Gas phase reactorsmay comprise fluidized bed reactors or staged horizontal reactors.Slurry reactors may comprise vertical and/or horizontal loops. Highpressure reactors may comprise autoclave and/or tubular reactors.Reactor types may include batch and/or continuous processes. Continuousprocesses may use intermittent and/or continuous product discharge ortransfer. Processes may also include partial or full direct recycle ofun-reacted monomer, un-reacted comonomer, catalyst and/or co-catalysts,diluents, and/or other materials of the polymerization process.

Polymerization reactor systems of the present disclosure may compriseone type of reactor in a system or multiple reactors of the same ordifferent type, operated in any suitable configuration. Production ofpolymers in multiple reactors may include several stages in at least twoseparate polymerization reactors interconnected by a transfer systemmaking it possible to transfer the polymers resulting from the firstpolymerization reactor into the second reactor. Alternatively,polymerization in multiple reactors may include the transfer, eithermanual or automatic, of polymer from one reactor to subsequent reactoror reactors for additional polymerization. Alternatively, multi-stage ormulti-step polymerization may take place in a single reactor, whereinthe conditions are changed such that a different polymerization reactiontakes place.

The desired polymerization conditions in one of the reactors may be thesame as or different from the operating conditions of any other reactorsinvolved in the overall process of producing the polymer of the presentdisclosure. Multiple reactor systems may include any combinationincluding, but not limited to multiple loop reactors, multiple gas phasereactors, a combination of loop and gas phase reactors, multiple highpressure reactors or a combination of high pressure with loop and/or gasreactors. The multiple reactors may be operated in series or inparallel. In an embodiment, any arrangement and/or any combination ofreactors may be employed to produce the polymer of the presentdisclosure.

According to one embodiment, the polymerization reactor system maycomprise at least one loop slurry reactor. Such reactors may comprisevertical or horizontal loops. Monomer, diluent, catalyst system, andoptionally any comonomer may be continuously fed to a loop slurryreactor, where polymerization occurs. Generally, continuous processesmay comprise the continuous introduction of a monomer, a catalyst,and/or a diluent into a polymerization reactor and the continuousremoval from this reactor of a suspension comprising polymer particlesand the diluent. Reactor effluent may be flashed to remove the liquidsthat comprise the diluent from the solid polymer, monomer and/orcomonomer. Various technologies may be used for this separation stepincluding but not limited to, flashing that may include any combinationof heat addition and pressure reduction; separation by cyclonic actionin either a cyclone or hydrocyclone; separation by centrifugation; orother appropriate method of separation.

Suitable slurry polymerization processes (also known as particle-formprocesses) are disclosed in U.S. Pat. Nos. 3,248,179, 4,501,885,5,565,175, 5,575,979, 6,239,235, 6,262,191 and 6,833,415, for example;each of which are herein incorporated by reference in their entirety.

Suitable diluents used in slurry polymerization include, but are notlimited to, the monomer being polymerized and hydrocarbons that areliquids under reaction conditions. Examples of suitable diluentsinclude, but are not limited to, hydrocarbons such as propane,cyclohexane, isobutane, n-butane, n-pentane, isopentane, neopentane, andn-hexane. Some loop polymerization reactions can occur under bulkconditions where no diluent is used. An example is polymerization ofpropylene monomer as disclosed in U.S. Pat. No. 5,455,314, which isincorporated by reference herein in its entirety.

According to yet another embodiment, the polymerization reactor maycomprise at least one gas phase reactor. Such systems may employ acontinuous recycle stream containing one or more monomers continuouslycycled through a fluidized bed in the presence of the catalyst underpolymerization conditions. A recycle stream may be withdrawn from thefluidized bed and recycled back into the reactor. Simultaneously,polymer product may be withdrawn from the reactor and new or freshmonomer may be added to replace the polymerized monomer. Such gas phasereactors may comprise a process for multi-step gas-phase polymerizationof olefins, in which olefins are polymerized in the gaseous phase in atleast two independent gas-phase polymerization zones while feeding acatalyst-containing polymer formed in a first polymerization zone to asecond polymerization zone. One type of gas phase reactor is disclosedin U.S. Pat. Nos. 4,588,790, 5,352,749, and 5,436,304, each of which isincorporated by reference in its entirety herein.

According to still another embodiment, a high pressure polymerizationreactor may comprise a tubular reactor or an autoclave reactor. Tubularreactors may have several zones where fresh monomer, initiators, orcatalysts are added. Monomer may be entrained in an inert gaseous streamand introduced at one zone of the reactor. Initiators, catalysts, and/orcatalyst components may be entrained in a gaseous stream and introducedat another zone of the reactor. The gas streams may be intermixed forpolymerization. Heat and pressure may be employed appropriately toobtain optimal polymerization reaction conditions.

According to yet another embodiment, the polymerization reactor maycomprise a solution polymerization reactor wherein the monomer iscontacted with the catalyst composition by suitable stirring or othermeans. A carrier comprising an organic diluent or excess monomer may beemployed. If desired, the monomer may be brought in the vapor phase intocontact with the catalytic reaction product, in the presence or absenceof liquid material. The polymerization zone is maintained attemperatures and pressures that will result in the formation of asolution of the polymer in a reaction medium. Agitation may be employedto obtain better temperature control and to maintain uniformpolymerization mixtures throughout the polymerization zone. Adequatemeans are utilized for dissipating the exothermic heat ofpolymerization.

Polymerization reactors suitable for the present disclosure may furthercomprise any combination of at least one raw material feed system, atleast one feed system for catalyst or catalyst components, and/or atleast one polymer recovery system. Suitable reactor systems for thepresent invention may further comprise systems for feedstockpurification, catalyst storage and preparation, extrusion, reactorcooling, polymer recovery, fractionation, recycle, storage, loadout,laboratory analysis, and process control.

Conditions that are controlled for polymerization efficiency and toprovide polymer properties include, but are not limited to temperature,pressure, type and quantity of catalyst or co-catalyst, and theconcentrations of various reactants. Polymerization temperature canaffect catalyst productivity, polymer molecular weight and molecularweight distribution. Suitable polymerization temperatures may be anytemperature below the de-polymerization temperature, according to theGibbs Free Energy Equation. Typically, this includes from about 60° C.to about 280° C., for example, and/or from about 70° C. to about 110°C., depending upon the type of polymerization reactor and/orpolymerization process.

Suitable pressures will also vary according to the reactor andpolymerization process. The pressure for liquid phase polymerization ina loop reactor is typically less than 1000 psig. Pressure for gas phasepolymerization is usually at about 200-500 psig. High pressurepolymerization in tubular or autoclave reactors is generally run atabout 20,000 to 75,000 psig. Polymerization reactors can also beoperated in a supercritical region occurring at generally highertemperatures and pressures. Operation above the critical point of apressure/temperature diagram (supercritical phase) may offer advantages.

The concentration of various reactants can be controlled to producepolymers with certain physical and mechanical properties. The proposedend-use product that will be formed by the polymer and the method offorming that product may be varied to determine the desired finalproduct properties. Mechanical properties include, but are not limitedto tensile strength, flexural modulus, impact resistance, creep, stressrelaxation and hardness tests. Physical properties include, but are notlimited to density, molecular weight, molecular weight distribution,melting temperature, glass transition temperature, temperature melt ofcrystallization, density, stereoregularity, crack growth, short chainbranching, long chain branching and rheological measurements.

The concentrations of monomer, co-monomer, hydrogen, co-catalyst,modifiers, and electron donors are generally important in producingspecific polymer properties. Comonomer may be used to control productdensity. Hydrogen may be used to control product molecular weight.Co-catalysts may be used to alkylate, scavenge poisons and/or controlmolecular weight. The concentration of poisons may be minimized, aspoisons may impact the reactions and/or otherwise affect polymer productproperties. Modifiers may be used to control product properties andelectron donors may affect stereoregularity.

In an embodiment, a method of preparing a PARPOL comprises contacting anolefin (e.g., ethylene) monomer with a catalyst system under conditionssuitable for the formation of a polymer of the type described herein. Inan embodiment, the catalyst system comprises a transition-metal complex.The terms “catalyst composition,” “catalyst mixture,” “catalyst system,”and the like, do not depend upon the actual product resulting from thecontact or reaction of the components of the mixtures, the nature of theactive catalytic site, or the fate of the co-catalyst, the catalyst, anyolefin monomer used to prepare a precontacted mixture, or theactivator-support, after combining these components. Therefore, theterms “catalyst composition,” “catalyst mixture,” “catalyst system,” andthe like, can include both heterogeneous compositions and homogenouscompositions.

In an embodiment, a catalyst system suitable for the preparation of aPARPOL comprises a metallocene-containing catalyst. Nonlimiting examplesof metallocene-containing catalysts suitable for use in this disclosureare described in more detail in U.S. Pat. Nos. 4,939,217; 5,191,132;5,210,352; 5,347,026; 5,399,636; 5,401,817; 5,420,320; 5,436,305;5,451,649; 5,496,781; 5,498,581; 5,541,272; 5,554,795; 5,563,284;5,565,592; 5,571,880; 5,594,078; 5,631,203; 5,631,335; 5,654,454;5,668,230; 5,705,478; 5,705,579; 6,187,880; 6,509,427; 7,026,494, andU.S. Patent App. No. 20100190926 A1, each of which is incorporated byreference herein in its entirety. Other processes to prepare metallocenecompounds suitable for use in this disclosure have been reported inreferences such as: Koppl, A. Alt, H. G. J. Mol. Catal. A. 2001, 165,23; Kajigaeshi, S.; Kadowaki, T.; Nishida, A.; Fujisaki, S. The ChemicalSociety of Japan, 1986, 59, 97; Alt, H. G.; Jung, M.; Kehr, G. J.Organomet. Chem. 1998, 562, 153-181; and Alt, H. G.; Jung, M. J.Organomet. Chem. 1998, 568, 87-112; each of which is incorporated byreference herein in its entirety. The following treatises also describesuch methods: Wailes, P. C.; Coutts, R. S. P.; Weigold, H. inOrganometallic Chemistry of Titanium, Zirconium, and Hafnium, Academic;New York, 1974; Cardin, D. J.; Lappert, M. F.; and Raston, C. L.;Chemistry of Organo-Zirconium and -Hafnium Compounds; Halstead Press;New York, 1986.

In an embodiment, a catalyst system suitable for the preparation of aPARPOL comprises a Ziegler-Natta catalyst. Nonlimiting examples ofZiegler-Natta catalysts suitable for use in this disclosure aredescribed in more detail in U.S. Pat. Nos. 6,174,971 and 6,486,274, eachof which is incorporated by reference herein in its entirety.

In an embodiment, a catalyst system suitable for the preparation of aPARPOL comprises a chromium-based catalyst. Nonlimiting examples ofchromium-based catalysts suitable for use in this disclosure aredescribed in more detail in U.S. Patent App. Nos. 20100113851 A1 and20110201768 A1, each of which is incorporated by reference herein in itsentirety. Chromium catalysts are used throughout the world for thepolymerization of polyethylene. Catalyst manufacturers prepare thecatalysts, often by placing the chromium on a solid support, such asalumina, silica, aluminophosphate, silica-alumina, silica-titania,silica-zirconia, clay, etc. The support helps to stabilize the activityof the chromium and allows the catalyst to be shipped in an inactiveform to the purchaser. Once the catalyst arrives at a polymermanufacturing site, it must be activated for use in the polymerizationprocess. Typically, chromium catalysts are activated by calcining orheating large quantities of the catalyst in dry air, in some type ofactivation apparatus of vessel such as a fluidized bed activator. Thefollowing references are incorporated as examples of chromium catalyststhat are suitable for use in the present disclosure: U.S. Pat. Nos.3,887,494, 3,119,569, 4,081,407, 4,152,503, 4,053,436, 4,981,831,4,364,842, 4,444,965, 4,364,855, 4,504,638, 3,900,457, 4,294,724,4,382,022, 4,151,122, 4,247,421, 4,248,735, 4,277,587, 4,177,162,4,735,931, 4,820,785, and 4,966,951.

The PARPOL may comprise additives. Examples of additives include, butare not limited to, antistatic agents, colorants, stabilizers,nucleators, surface modifiers, pigments, slip agents, antiblocks,tackifiers, polymer processing aids, and combinations thereof. In anembodiment, the polymeric composition comprises carbon black. Suchadditives may be used singularly or in combination and may be includedin the polymer composition before, during, or after preparation of thePARPOL composition as described herein. Such additives may be added viaany suitable technique, for example during an extrusion or compoundingstep such as during pelletization or subsequent processing into an enduse article. Such additives may be added to the polymer before, during,and/or after the reactive extrusion process described herein (e.g.,additives may be added to the PARPOL before reactive extrusion,additives may be added to the PARPOL during reactive extrusion,additives may be added to the resultant radically coupled resin (i.e.,RCR) form from reactive extrusion, or combinations thereof).

A PARPOL (and likewise a resultant RCR) may be further described byreference to one or more parameters such as density, molecular weight,molecular weight distribution, modality, melt index, high load meltindex, Carreau-Yasuda “a” parameter, zero shear viscosity, relaxationtime, degree of branching (e.g., short and/or long chain branching), anddegree of unsaturation. While each of these parameters is describedgenerally, it is understood that each such parameter and combinationsthereof is applicable to any particular PARPOL of the type disclosedherein such as, by way of non-limiting examples, polyolefin homopolymers{e.g., polyethylene homopolymers, polyalphaolefins (PAO)}, copolymers(e.g., copolymers of ethylene and propene, 1-butene, 1-pentene,1-hexene, 1-heptene, 1-octene, etc.).

In an embodiment, a PARPOL of the type described herein is characterizedby a density of from about 0.89 g/cc to about 0.98 g/cc, alternativelyfrom about 0.915 g/cc to about 0.975 g/cc, or alternatively from about0.925 g/cc to about 0.975 g/cc, as determined in accordance with ASTMD1505.

In an embodiment, a PARPOL of the type described herein may becharacterized by a weight average molecular weight (M_(w)) of less thanabout 100,000 g/mol., alternatively from about 350 g/mol to about 50,000g/mol, alternatively from about 1,000 g/mol to about 40,000 g/mol;alternatively from about 10,000 g/mol to about 40,000 g/mol; oralternatively from about 25,000 g/mol to about 40,000 g/mol; a numberaverage molecular weight (M_(n)) of from about 100 g/mol to about 40,000g/mol, alternatively from about 5000 g/mol to about 40,000 g/mol;alternatively from about 100 g/mol to about 20,000 g/mol; alternativelyfrom about 100 g/mol to about 16,000 g/mol; or alternatively from about500 g/mol to about 16,000 g/mol; alternatively from about 1,250 g/mol toabout 16,000 g/mol; and a z-average molecular weight (M_(z)) of fromabout 1,400 g/mol to about 1,5000,000 g/mol, alternatively from about400,000 g/mol to about 1,500,000 g/mol, alternatively from about 1,400g/mol to about 750,000 g/mol; alternatively from about 4,000 g/mol toabout 600,000 g/mol; alternatively from about 40,000 g/mol to about600,000 g/mol; or alternatively from about 100,000 g/mol to about600,000 g/mol. The M_(w) describes the size average of a polymercomposition and can be calculated according to equation 1:

$\begin{matrix}{M_{w} = \frac{\sum\limits_{i}\;{N_{i}M_{i}^{2}}}{\sum\limits_{i}\;{N_{i}M_{i}}}} & (1)\end{matrix}$wherein N_(i) is the number of molecules of molecular weight M_(i). Allmolecular weight averages are expressed in gram per mole (g/mol) orDaltons (Da). The M_(n) is the common average of the molecular weightsof the individual polymers calculated by measuring the molecular weightM_(i) of N_(i) polymer molecules, summing the weights, and dividing bythe total number of polymer molecules, according to equation 2:

$\begin{matrix}{M_{n} = \frac{\sum\limits_{i}\;{N_{i}M_{i}}}{\sum\limits_{i}\; N_{i}}} & (2)\end{matrix}$The M_(z) is a higher order molecular weight average which is calculatedaccording to equation 3:

$\begin{matrix}{M_{z} = \frac{\sum\limits_{i}\;{N_{i}M_{i}^{3}}}{\sum\limits_{i}\;{N_{i}M_{i}^{2}}}} & (3)\end{matrix}$wherein N_(i) is the number of molecules of molecular weight M_(i).

The molecular weight distribution (MWD) of the PARPOL may becharacterized by the ratio of the M_(w) to the M_(n) which is alsoreferred to as the polydispersity index (PDI) or more simply aspolydispersity. A PARPOL of the type disclosed herein may have a PDIfrom about 1 to about 50, alternatively from about 2 to about 10,alternatively from about 2 to about 5, or alternatively from about 2 toabout 3.

The ratio of M_(z) to the M_(w) is another indication of the breadth ofthe MWD of a polymer. A PARPOL of the type described herein may befurther characterized by a ratio (M_(Z)/M_(W)) of from about 1.3 toabout 15, alternatively from about 1.5 to about 12, or alternativelyfrom about 2 to about 10.

A PARPOL of the type described herein may be a multimodal polymer.Herein, the “modality” of a polymer refers to the form of its molecularweight distribution curve, i.e., the appearance of the graph of thepolymer weight fraction, frequency, or number as a function of itsmolecular weight, as may be displayed by, for example, gel permeationchromatography (GPC). The polymer weight fraction refers to the weightfraction of molecules of a given size. A polymer having a molecularweight distribution curve showing a single peak may be referred to as aunimodal polymer, a polymer having a curve showing two distinct peaksmay be referred to as a bimodal or a bimodal-like polymer, a polymerhaving a curve showing three distinct peaks may be referred to as atrimodal polymer, etc. Polymers having molecular weight distributioncurves showing more than one peak may be collectively referred to asmultimodal polymers or resins. It is acknowledged that, in someinstances, a multimodal polymer may appear to have a single peak via,for example, GPC analysis, when in fact the polymer itself ismultimodal. In such instances, overlap of peaks may obscure the presenceof other peaks and may imply unimodality, when in fact multimodality isa more accurate representation of the nature of the polymer or polymers.

In an embodiment, the PARPOL is characterized as a bimodal polymer. Sucha bimodal PARPOL may display two distinct peaks attributable to a highermolecular weight (HMW) component and a lower molecular weight (LMW)component. In an embodiment, the LMW component has a M_(w) ranging fromabout 350 g/mol to about 100,000 g/mol, alternatively from about 1,000g/mol to about 40,000 g/mol, alternatively from about 10,000 g/mol toabout 40,000 g/mol, or alternatively from about 25,000 g/mol to about40,000 g/mol and is present in the PARPOL composition in an amount offrom about 0 weight percent (wt. %) to less than about 100 wt. %,alternatively from about 50 wt. % to about 100 wt. %, or alternativelyfrom about 75% to about 100 wt. %, based on the total polymer weight. Inan embodiment, the HMW component has a M_(w) ranging from about 40,000g/mol to about 100,000 g/mol, alternatively from about 50,000 g/mol toabout 100,000 g/mol, or alternatively from about 75,000 g/mol to about100,000 g/mol and is present in the PARPOL composition in an amount offrom greater than about 0 wt. % to less than about 100 wt. %,alternatively from about 25 wt. % to about 100 wt. %, or alternativelyfrom about 50 wt. % to about 100 wt. %, based on the total polymerweight.

In an embodiment, a PARPOL of the type described herein may becharacterized by a melt index, MI, equal to or greater than about 10dg/min, alternatively equal to or greater than about 50 dg/min,alternatively equal to or greater than about 100 dg/min, oralternatively equal to or greater than about 200 dg/min. The melt index(MI) refers to the amount of a polymer which can be forced through anextrusion rheometer orifice of 0.0825 inch diameter when subjected to aforce of 2,160 grams in ten minutes at 190° C., as determined inaccordance with ASTM D1238.

In an embodiment, a PARPOL of the type described herein may becharacterized by a high load melt index, HLMI, equal to or greater thanabout 100 dg/min, alternatively in the range of from about 100 dg/min toabout 5000 dg/min, alternatively from about 500 dg/min to about 5000dg/min, or alternatively from about 750 dg/min to about 5000 dg/min. TheHLMI represents the rate of flow of a molten polymer through an orificeof 0.0825 inch diameter when subjected to a force of 21,600 grams at190° C. as determined in accordance with ASTM D1238.

In an embodiment, a PARPOL of the type described herein may becharacterized by a shear response in the range of from about 10 to about500, alternatively from about 10 to about 50, or alternatively fromabout 10 to about 20. The shear response refers to the ratio of highload melt index to melt index (HLMI/MI).

In an embodiment, a PARPOL of the type described herein may becharacterized by a Carreau-Yasuda ‘a’ parameter in the range of fromabout 0 to about 2.0, alternatively from about 0.1 to about 1.0, oralternatively from about 0.05 to about 0.8. The Carreau-Yasuda ‘a’parameter (CY-a) is defined as the rheological breadth parameter.Rheological breadth refers to the breadth of the transition regionbetween Newtonian and power-law type shear rate for a polymer or thefrequency dependence of the viscosity of the polymer. The rheologicalbreadth is a function of the relaxation time distribution of a polymer,which in turn is a function of the polymer molecular structure orarchitecture. The CY-a parameter may be obtained by assuming theCox-Merz rule and calculated by fitting flow curves generated inlinear-viscoelastic dynamic oscillatory frequency sweep experiments witha modified Carreau-Yasuda (CY) model, which is represented by equation4:

$\begin{matrix}{{{\eta^{*}(\omega)}} = {\eta_{o}\left\lbrack {1 + \left( {\tau_{\eta}\omega} \right)^{a}} \right\rbrack}^{\frac{n - 1}{a}}} & (4)\end{matrix}$

where

|η*(ω)|=magnitude of the complex shear viscosity (Pa·s)

η_(o)=zero shear viscosity (Pa·s) [defines the Newtonian plateau]

ω=angular frequency of oscillatory shear deformation (i.e., shear rate(1/s))

a=rheological breadth parameter

τ_(η)=viscous relaxation time (s) [describes the location in time of thetransition region]

n=power law constant [defines the final slope of the high shear rateregion].

To facilitate model fitting, the power law constant n is held at aconstant value (i.e., 0.1818). The dynamic shear viscosities may bemeasured experimentally, and the data may be fit to the CY equation 4 todetermine η_(o) values and other rheological parameters. Details of thesignificance and interpretation of the CY model and derived parametersmay be found in: C. A. Hieber and H. H. Chiang, Rheol. Acta, 28, 321(1989); C. A. Hieber and H. H. Chiang, Polym. Eng. Sci., 32, 931 (1992);and R. B. Bird, R. C. Armstrong and O. Hasseger, Dynamics of PolymericLiquids, Volume 1, Fluid Mechanics, 2nd Edition, John Wiley & Sons(1987), each of which is incorporated by reference herein in itsentirety.

The zero shear viscosity refers to the viscosity of the polymer at azero shear rate and is indicative of the molecular structure of thematerials. Further, for polymer melts, the zero shear viscosity is oftena useful indicator of processing attributes such as melt strength inblow-molding and foam technologies and bubble stability in film blowing.For example, the higher the zero shear viscosity, the better the meltstrength or bubble stability. In an embodiment, a PARPOL of the typedescribed herein may be characterized by a zero shear viscosity (η_(o)),defined by equation 4, in the range of from about 1.0E+00 Pa-s to about1.0E+06 Pa-s, alternatively from about 1.0E+00 Pa-s to about 1.0E+05Pa-s, or alternatively from about 1.0E+00 Pa-s to about 1.0E+03 Pa-s.

In an embodiment, a PARPOL of the type described herein has a relaxationtime (τ_(n)), defined by Equation (4), in the range of from about1.0E−03 s to about 1.0E+08 s, alternatively, from about 1.0E−02 s toabout 1.2E+04 s, or alternatively, from about 1.0E−02 s to about 1.0E+03s. The relaxation rate refers to the viscous relaxation times of thepolymer and is indicative of a distribution of relaxation timesassociated with the wide distribution of molecular weights.

A PARPOL of the type disclosed herein may be further characterized bythe degree and nature of branching present in the individual componentsof the polymer composition and/or in the polymer composition as a whole.Short chain branching (SCB) is known for its effects on polymerproperties such as stiffness, tensile properties, heat resistance,hardness, permeation resistance, shrinkage, creep resistance,transparency, stress crack resistance, flexibility, impact strength, andthe solid state properties of semi-crystalline polymers such aspolyethylene. For the purpose of this disclosure, SCB is defined ascomprising chains that have a number of carbon atoms ranging from about1 carbon atom to about 20 carbon atoms, alternatively from about 1carbon atoms to about 10 carbon atoms, or alternatively from about 1carbon atoms to about 6 carbon atoms.

SCB content may be determined as the number of SCB per 1,000 carbonatoms (SCB/10³ carbons). In an embodiment, a PARPOL of the typedescribed herein may display short chain branching (for the compositionas a whole) per 1,000 carbon atoms in the range of from about 0 carbonto about 40 carbons, alternatively from about 0 carbon to about 35carbons, or alternatively from about 0 carbon to about 25 carbons.Short-chain branching may be determined using any suitable methodologysuch as gas permeation chromatography or size exclusion chromatographycoupled with Fourier transform infrared.

In an embodiment, a PARPOL of the type described herein may becharacterized as a branched polymer wherein the level of long chainbranching (LCB) present in the polymer is low. For the purpose of thisdisclosure, LCB is defined as comprising chains that have a number ofcarbon atoms ranging from about 50 carbon atoms to about 11,000 carbonatoms, alternatively from about 75 carbon atoms to about 9,000 carbonatoms, or alternatively from about 100 carbon atoms to about 7,200carbon atoms. Polymer chain branching may be measured using any suitablemethodology such as nuclear magnetic resonance (NMR) or size-exclusionchromatography-multiangle light scattering technique (SEC-MALS). Methodsfor the determination of long chain branching distribution are describedin more detail in Polymer (2005) Volume 46, Issue 14, Pages 5165-5182,which is incorporated by reference herein in its entirety.

In an embodiment, a PARPOL of the type disclosed herein may becharacterized by a high degree of unsaturation when compared to Ziegleror chromium derived polyethylene resins. Without wishing to be limitedby theory, generally, there are four types of olefinic groups present insufficient concentrations in polyethylene polymers to warrantconsideration, one or more of which can normally be found in anypolyethylene: (i) vinyl unsaturation, R—CH═CH₂, which may also bereferred to as terminal unsaturation; (ii) trans-vinylene unsaturation,R—CH═CH—R′, which may also be referred to as transinternal unsaturation,or trans unsaturation; and (iii) cis-vinylidene unsaturation and (iv)vinylidene or pendent methylene unsaturation, RR′C═CH₂. Vinylunsaturation may be expressed as the number of vinyl groups present per1,000 carbon atoms and determined in accordance with ASTM D6248. Bothcis- and trans-unsaturation may be expressed as the number oftrans-vinylidene groups present per 1,000 carbon atoms and determined inaccordance with ASTM D6248. Vinylidene unsaturation may be expressed asthe number of cis- or trans-vinylidene groups present per 1,000 carbonatoms and determined in accordance with ASTM D3124. The total degree ofunsaturation of a polymer may be calculated as follows: totalunsaturation=vinyl unsaturation+cis unsaturation+transunsaturation+vinylidene unsaturation. The total unsaturation representsthe total number of unsaturated groups present per 1,000 carbon atoms.

In an embodiment, a PARPOL of the type disclosed herein may becharacterized by a vinyl unsaturation per 1000 carbon atoms of fromabout 0 to about 10, alternatively from about 0 to about 5, oralternatively from about 0 to about 2. In an embodiment, a PARPOL of thetype disclosed herein may be characterized by a trans unsaturation offrom about 0 to about 3, alternatively from about 0 to about 2, oralternatively from about 0 to about 1. In an embodiment, a PARPOL of thetype disclosed herein may be characterized by a vinylidene unsaturationof from about 0 to about 0.5, alternatively from about 0 to about 0.4,or alternatively from about 0 to about 0.3. In an embodiment, a PARPOLof the type disclosed herein may be characterized by a totalunsaturation of from about 0 to about 14, alternatively from about 0 toabout 7, or alternatively from about 0 to about 3.

In an embodiment, a PARPOL of the type described herein may be subjectedto one or more procedures for increasing the level of long chainbranching and/or unsaturation. In an embodiment, a procedure forincreasing the level of long chain branching in a PARPOL comprisesradical coupling. In an embodiment, a radically coupled resin (RCR) maybe produced by reactive extrusion of a mixture comprising a PARPOL ofthe type disclosed herein, a coupling compound, and an optional coagent.

In an embodiment, the mixture comprises a coupling compound. Couplingcompounds suitable for use in the mixture comprise organic peroxides,azides, azo compounds, silanes, or combinations thereof.

Nonlimiting examples of organic peroxides suitable for use in thisdisclosure include dialkyl peroxides, dicumyl peroxide, di-t-butylperoxide, 2,5-dimethyl-2,5-di-(t-butylperoxy) hexane (DHBP), diacylperoxides, dilauroyl peroxide, dibenzoyl peroxide, peroxyesters, t-butylperoxy-2-ethylhexanoate, OO-(t-butyl)-O-(2-ethylhexyl)peroxycarbonate,t-butyl peroxy-3,5,5-trimethylhexylhexanoate, t-butyl peroxy benzoate,diperoxyketals, diacyl peroxides, t-amyl peroxides,n-butyl-4,4-di-(t-butyl peroxy)valerate, and the like, or combinationsthereof.

Nonlimiting examples of azides suitable for use in this disclosureinclude R—N₃, R—C(O)—N₃, R—O—C(O)—N₃, (RO₂)—(PO)—N₃, R₂P(O)—N₃,R₃—Si—N₃, R—SO₂—N₃, or combinations thereof, wherein R can be anunsubstituted or inertly substituted alkyl, aryl, ether, siloxane,silane, heterocycle, haloalkyl, haloaryl, or any combination thereof.

Nonlimiting examples of azo compounds suitable for use in thisdisclosure include R¹—N₂—R² compounds, wherein R¹ and R² can eachindependently be an unsubstituted or inertly substituted alkyl, aryl,ether, siloxane, silane, heterocycle, haloalkyl, haloaryl, or anycombination thereof.

In an embodiment, the coupling compound is present in the mixture in anamount of from about 0.001 wt. % to about 10 wt. %, alternatively fromabout 0.01 wt. % to about 5 wt. %, alternatively from about 0.1 wt. % toabout 5 wt. %, or alternatively from about 0.5 wt. % to about 3 wt. %,based on the total weight of the mixture.

In an embodiment, the mixture comprises a coagent. Without wishing to belimited by theory, a coagent is a compound that facilitates theformation of a higher concentration of reactive sites. Manynonproductive reactions such as polymer scission or other deleteriousreactions are kinetically favored, and typically only a very highconcentration of reactive sites (e.g., radical sites) on the polymerbackbone allows for effective product formation to occur at all.Generally, the coagent increases the local concentration of highlyreactive groups (e.g., radicals). In an embodiment, the coagentcomprises a Type I coagent, a Type II coagent or combinations thereof.

Herein, a Type I coagent refers to polar low molecular weight (e.g.,less than about 500 g/mol) compounds which form radicals throughaddition reactions. In an embodiment, the Type I coagent comprisesmultifunctional acrylates, multifunctional methacrylates, dimaleimides,or combinations thereof. Examples of Type I coagents suitable for use inthe present disclosure include without limitation trimethylolpropanetriacrylate, trimethylolpropane trimethacrylate, ethylene glycoldiacrylate, N,N′-m-phenylene dimaleimide, zinc diacrylate and zincdimethacrylate.

Herein, a Type II coagent refers to materials that form radicalsprimarily through hydrogen abstraction. Type II coagents suitable foruse in the present disclosure include without limitationallyl-containing cyanurates, isocyanurates, phthalates, homopolymers ofdienes, copolymers of dienes, vinyl aromatics or combinations thereof.Examples of Type II coagents suitable for use in the present disclosureinclude without limitation triallyl cyanurate (TAC),tri-allyl-iso-cyanurate, pentaerythriol triacrylate, p-benzoquinone,vinyl poly(butadiene), vinyl styrene-butadiene copolymer.

In an embodiment, the optional coagent is present in the mixture in anamount of from about 0 wt. % to about 10 wt. %, alternatively from about0 wt. % to about 5 wt. %, alternatively from about 0 wt. % to about 1wt. %, or alternatively from about 0 wt. % to about 0.5 wt. %, based onthe total weight of the mixture.

Reactive extrusion is a polymer processing technique that involves theuse of a polymer extruder as a chemical reactor in which individualcomponents may be bonded by a chemical reaction while inside theextruder. Typical reactive extruders consist of one or two horizontalscrews that may be rotated by the use of a motor attached to one end ofa screw. The reactive extruder may be thermostated at a certaintemperature across the entire lengths, or it may have a temperaturegradient applied across its length, according to a desired temperatureprofile. Without wishing to be limited by theory, the residence time ofa reactive extruder may be defined as the time spent inside the extruderby the components that are fed into the reactive extruder.

In an embodiment, the temperature profile (i.e., temperature gradientapplied across its length) during the reactive extrusion process rangesfrom about 120° C. to about 300° C., alternatively from about 145° C. toabout 250° C., alternatively from about 145° C. to about 230° C., oralternatively from about 190° C. to about 215° C.

In an embodiment, the residence time during the reactive extrusionprocess ranges from about 1 s to about 10 min, alternatively from about5 s to about 5 min, alternatively from about 10 s to about 3 min, oralternatively from about 10 s to about 2 min.

Reactive extrusion of mixtures of the type disclosed herein is generallythought to result in the formation of free radicals. Free radicals mayform on the PARPOL chain, by homolytic cleavage of a C—H bond. Withoutwishing to be limited theory, homolytic cleavage or homolysis of acovalent bond involves the equal distribution of the 2 electrons formingthe covalent bond to each of the two atoms that originally formed thecovalent bond, thus forming two free radicals. Thus, subjecting amixture of the type disclosed herein to reactive extrusion may result inthe formation of carbon atom radicals, C., on the PARPOL chain backbone,via a homolytic cleavage mechanism. Reactive extrusion of a mixture ofthe type disclosed herein may result in the formation of carbon atomradicals on the PARPOL chain backbone which react with other suchspecies in a carbon-carbon coupling reaction to form a branched polymerhaving a higher molecular weight than the PARPOL.

During the residence time of the mixture subjected to the reactiveextrusion process, homolytic cleavage followed by carbon-carbon couplingreactions of the free radical polymers may occur repeatedly. The productof the reactive extrusion process (i.e., radically coupled resin) mayexhibit a highly branched architecture along with a molecular weightthat is greater than the PARPOL as depicted in SEC-MALS data (videinfra). In an embodiment, the RCR has a M_(w) that is greater than thatof the PARPOL by about 20% to about 1,000%, alternatively from about 50%to about 800%, alternatively from about 75% to about 700%, oralternatively from about 100% to about 600%, based on the molecularweight of the PARPOL.

In an embodiment, the PARPOL is a homopolymer (e.g., a polyethylenehomopolymer) and the product RCR is a radically coupled homopolymerresin and designated RCR_(homo). In another embodiment, the PARPOL is acopolymer (e.g., a copolymer of ethylene and 1-hexene) and the productRCR is a radically coupled copolymer resin and designated RCR_(cop). Inyet another embodiment, the PARPOL has a molecular weight of greaterthan about 20,000 g/mol and the product RCR is a radically coupledhigher molecular weight resin RCR_(HMW). It is to be understood that theRCR_(homo), RCR_(cop) and RCR_(HMW) are collectively referred to asRCRs.

In an embodiment, a RCR of the type described herein may becharacterized by a M_(w) of from about 50,000 g/mol to about 250,000g/mol, alternatively from about 60,000 g/mol to about 175,000 g/mol;alternatively from about 65,000 g/mol to about 160,000 g/mol; oralternatively from about 70,000 g/mol to about 150,000 g/mol; a M_(n) offrom about 2,000 g/mol to about 62,500 g/mol, alternatively from about2,400 g/mol to about 43,750 g/mol; alternatively from about 2,600 g/molto about 40,000 g/mol; or alternatively from about 2,800 g/mol to about37,500 g/mol and a M_(z) of from about 200,000 g/mol to about 3,750,000g/mol, alternatively from about 240,000 g/mol to about 2,625,000 g/mol;alternatively from about 260,000 g/mol to about 2,400,000 g/mol; oralternatively from about 280,000 g/mol to about 2,250,000 g/mol.

In an embodiment, a RCR of the type described herein may becharacterized by a PDI of from about 4 to about 40, alternatively fromabout 4 to about 20, or alternatively from about 6 to about 18.

In an embodiment, the RCR is a RCR_(homo) and is characterized by a PDIof from about 4 to about 30, alternatively from about 5 to about 25, oralternatively from about 14 to about 25.

In another embodiment, the RCR is an RCR_(cop) and is characterized by aPDI of from about 4 to about 20, alternatively from about 4 to about 15,or alternatively from about 4 to about 10.

In an embodiment, the RCR is a RCR_(homo) and is characterized by adensity of from about 0.89 g/cc to about 0.98 g/cc, alternatively fromabout 0.915 g/cc to about 0.975 g/cc, or alternatively from about 0.925g/cc to about 0.975 g/cc.

In another embodiment, the RCR is an RCR_(cop) and is characterized by adensity of from about 0.93 g/cc to about 0.975 g/cc, alternatively fromabout 0.94 g/cc to about 0.975 g/cc, alternatively from about 0.95 g/ccto about 0.975 g/cc, or alternatively from about 0.96 g/cc to about0.975 g/cc.

In yet another embodiment, the RCR is a RCR_(HMW) and is characterizedby a density of from about 0.89 g/cc to about 0.95 g/cc, alternativelyfrom about 0.89 g/cc to about 0.94 g/cc, or alternatively from about0.89 g/cc to about 0.93 g/cc.

In an embodiment, the RCR is a RCR_(homo) and is characterized by a meltindex, MI, of from about 0 dg/min to about 150 dg/min, alternativelyfrom about 0 dg/min to about 100 dg/min, alternatively from about 0dg/min to about 75 dg/min, or alternatively from about 0.4 dg/min toabout 45 dg/min.

In an embodiment, an RCR of the type described herein may becharacterized by a high load melt index, HLMI, in the range of fromabout 0.1 dg/min to about 500 dg/min, alternatively from about 10 dg/minto about 500 dg/min, or alternatively from about 25 dg/min to about 500dg/min.

In an embodiment, an RCR of the type described herein may becharacterized by a shear response (HLMI/MI) in the range of from about25 to about 600, alternatively from about 50 to about 500, alternativelyfrom about 75 to about 400, or alternatively from about 90 to about 250.

In an embodiment, an RCR of the type described herein may becharacterized by a Carreau-Yasuda ‘a’ parameter in the range of fromabout 0.005 to about 2.00, alternatively from about 0.01 to about 1.00,alternatively from about 0.05 to about 0.80, or alternatively from about0.10 to about 0.50.

In an embodiment, an RCR of the type described herein may becharacterized by a zero shear viscosity (η₀) in the range of from about1.0E+01 Pa-s to about 9.0E+10 Pa-s, alternatively from about 1.0E+02Pa-s to about 5.0E+08 Pa-s, alternatively from about 1.0E+03 Pa-s toabout 3.0E+07 Pa-s, or alternatively from about 1.0E+03 Pa-s to about2.0E+06 Pa-s.

In an embodiment, an RCR of the type described herein has a M_(w) offrom about 50 kDa to about 250 kDa, alternatively from about 60 kDa toabout 175 kDa, alternatively from about 65 kDa to about 160 kDa, oralternatively from about 70 kDa to about 150 kDA, and a zero shearviscosity that follows a quadratic function described by the equation:y=2E+09x²−1E+12x+6E+13), where x is the M. The quadratic function isderived from a hypothetical line in the Janzen-Colby graph.

In another embodiment, a RCR of the type described herein may have aM_(w) of from about 50 kDa to about 250 kDa, alternatively from about 60kDa to about 175 kDa, alternatively from about 65 kDa to about 160 kDa,or alternatively from about 70 kDa to about 170 kDa, and may becharacterized by a tan θ value that follows a logarithmic functiondescribed by (y=−0.072 ln(x)+0.40161), wherein x is the M_(w). Thelogarithmic function was developed by plotting tan delta versus weightaverage molecular weight for RCR_(HMW).

In an embodiment, an RCR of the type described herein may becharacterized as a branched polymer wherein the level of LCB present inthe polymer is elevated, when compared to the level of LCB in thePARPOL. In an embodiment, λ is in the range of from about 0.001 LCB/10³carbons to about 2 LCB/10³ carbons.

In an embodiment, λ, as measured by NMR for a RCR of the type disclosedherein, is in the range of from about 0.01 LCB/10³ carbons to about 2LCB/10³ carbons, alternatively from about 0.05 LCB/10³ carbons to about1.5 LCB/10³ carbons, alternatively from about 0.1 LCB/10³ carbons toabout 1.0 LCB/10³ carbons, or alternatively from about 0.2 LCB/10³carbons to about 0.4 LCB/10³ carbons.

Alternatively, in an embodiment, λ, as measured by SEC-MALS for an RCRof the type disclosed herein, is in the range of from about 0.001LCB/10³ carbons to about 1.5 LCB/10³ carbons, alternatively from about0.01 LCB/10³ carbons to about 1.0 LCB/10³ carbons, alternatively fromabout 0.1 LCB/10³ carbons to about 0.8 LCB/10³ carbons, or alternativelyfrom about 0.1 LCB/10³ carbons to about 0.5 LCB/10³ carbons.

R_(g) and M_(w) have a power-law relationship, i.e. R_(g)=K*M_(w) ^(a),where K and a are constants. The a-parameter for a linear polymer isalways larger than a branched polymer of same type. Under theexperimental condition, the a-parameter for the linear control is ca.0.6. The a-parameter for branched polymers is <0.6. In an embodiment,for an RCR of the type disclosed herein, at M_(w) in the range of fromabout 50 kDa to about 250 kDa, when subjected to SEC-MALS analysisdisplay an a-parameter ranging from about 0.25 to about 0.55,alternatively from about 0.30 to about 0.52, or alternatively from about0.35 to about 0.49.

In an embodiment, the RCR comprises at least two types of short chainbranches. The RCR may comprise ethyl, butyl, hexyl, 4-methylpentyl oroctyl short chain branches. In an embodiment, the RCR is an RCR_(homo).In such an embodiment, the RCR_(homo) may be characterized by shortchain branching per 1000 carbon atoms in the range of from about 0 toabout 40, alternatively from about 0 carbons to about 35, alternativelyfrom about 0 to about 30, or alternatively from about 0 to about 25.

In another embodiment, the RCR comprises an RCR_(cop). In suchembodiments, the RCR_(cop) may be characterized by short chain branchingin the range of from about 0 mol % carbons to about 10 mol %,alternatively from about 0 mol. % carbons to about 8 mol %,alternatively from about 0 mol % carbons to about 5 mol %, oralternatively from about 0 mol % carbons to about 2 mol %, based on ¹³CNMR spectroscopy.

In yet another embodiment, the RCR comprises a RCR_(HMW). In suchembodiment, the RCR_(HMW) may be characterized by short chain branchingin the range of from about 1 mol % carbons to about 10 mol %,alternatively from about 2 mol % carbons to about 10 mol %,alternatively from about 3 mol % carbons to about 10 mol %, oralternatively from about 4 mol % carbons to about 10 mol %, based on ¹³CNMR spectroscopy.

As will be appreciated by one of ordinary skill in the art, SCB inethylene polymers is typically the result of comonomer incorporation.The comonomers typically employed in the formation of ethylene polymerscontain an even number of carbon atoms (e.g., 1-hexene, 1-octene). RCRsof the type disclosed herein are characterized by SCB that is the resultof a radical coupling process producing branches that may contain an oddnumber of carbon atoms. In an embodiment, an RCR of the type disclosedherein contains SCB having an odd carbon atom number in an amount ofless than about 10%, alternatively less than about 7%, alternativelyless than about 5%, or alternatively less than about 3%.

In an embodiment, an RCR of the type disclosed herein having a M_(w)ranging from about 50 kDa to about 250 kDa, may be characterized by alevel of vinyl unsaturation per 1000 carbon atoms ranging from about 0to about 0.6, alternatively from about 0 to about 0.4, or alternativelyfrom about 0 to about 0.3. In an embodiment, an RCR of the typedisclosed having a M_(w) ranging from about 50 kDa to about 250 kDa maybe characterized by a level of trans unsaturation per 1000 carbon atomsranging from about 0 to about 0.08, alternatively from about oralternatively from about 0 to about 0.05.

In an embodiment, RCRs of the type disclosed herein display anactivation energy of from about 30 kJ mol⁻¹ to about 85 kJ mol⁻¹,alternatively from about 35 kJ mol⁻¹ to about 80 kJ mol⁻¹, alternativelyfrom about 35 kJ mol⁻¹ to about 75 kJ mol⁻¹, or alternatively from about38 kJ mol⁻¹ to about 65 kJ mol⁻¹. In another embodiment, RCRs of thetype disclosed herein display an activation energy from about 28 kJmol⁻¹ to about 85 kJ mol⁻¹, alternatively from about 35 kJ mol⁻¹ toabout 60 kJ mol⁻¹, alternatively from about 37 kJ mol⁻¹ to about 55 kJmol⁻¹, or alternatively from about 37 kJ mol⁻¹ to about 45 kJ mol⁻¹. Theactivation energy refers to complex thermorheological behavior and maybe calculated from rheological experiments measuring various parameterssuch as zero-shear viscosities at different temperatures.

An RCR of the type disclosed herein may be utilized in any suitableapplication. For example, RCRs of the type disclosed herein may findutility in non-linear optics, nanomaterials for host-guestencapsulation, fabrication of inorganic-organic hybrids, coatings,lubricants, adhesives, compatibilizers, rheology modifiers, curingadditives, dye carrier, dispersants, article production, cast and blownfilm applications.

EXAMPLES

The disclosure having been generally described, the following examplesare given as particular embodiments of the disclosure and to demonstratethe practice and advantages thereof. It is understood that the examplesare given by way of illustration and are not intended to limit thespecification or the claims in any manner.

Characterization

SEC-MALS Measurement

SEC-MALS is a combined method of size-exclusion chromatography (SEC),also known as gel-permeation chromatography (GPC), with multi-anglelight scattering (MALS). A DAWN EOS multi-angle light scatteringphotometer (Wyatt Technology) was attached to a Waters 150-CV plus GPCsystem through a transfer line thermally controlled at 145° C. At a setflow rate of 0.7 mL/min, the mobile phase 1,2,4-trichlorobenzene (TCB)containing 0.5 g/L of 2,6-di-tert-buty-1,4-methylphenol (BHT) was elutedthrough three (3) 7.5 mm×300 mm 20M Mixed A-LS columns (Polymer Labs,now an Agilent Company). PE solutions with nominal concentrations of 1.0mg/mL were prepared at 150° C. for 3-4 h before being transferred to SECinjection vials sitting in a carousel heated at 145° C. In addition to aconcentration chromatogram, seventeen (17) light scatteringchromatograms at different scattering angles were acquired for eachinjection. At each chromatographic slice, both the absolute molecularweight (M) and the root-mean square radius, commonly known as radius ofgyration, R_(g), were obtained from the Debye plot. The linear PEcontrol employed in this study was a high-density polyethylene (HDPE)with a broad molecular weight distribution (MWD) (CPChem Marlex™ 9640).The refractive index increment dn/dc used in this study is 0.097 mL/gfor PE in TCB at 135° C.

The DAWN EOS system was calibrated with neat toluene at room temperatureto convert the measured voltage to intensity of scattered light. Duringthe calibration, toluene was filtered with 0.02 um filter (Whatman) anddirectly passed through the flowcell of the MALS. At room temperature,the Rayleigh ratio at the given conditions was given by 1.406×10⁻⁵ cm⁻¹.A narrow polystyrene (PS) standard (American Polymer Standards) of MW of30,000 g/mol and a concentration of 5-10 mg/mL in TCB was employed tonormalize the system at 145° C. At the given chromatographic conditions,radius of gyration (R_(g)) of the polystyrene (PS) was estimated to be5.6 nm using Fox-Flory equation coupled with its Mark-Houwink exponentin the chromatographic conditions. A more detailed description of theSEC-MALS method can be found elsewhere.

Methods for the determination of short chain branching and long chainbranching distribution are described in more detail in Polymer (2005)Volume: 46, Issue: 14, Pages: 5165-5182, which is incorporated byreference herein in its entirety.

Rheology Measurements

Samples for melt viscosity measurement were compression molded at 182°C. for a total of three minutes. The samples were allowed to melt at arelatively low pressure for one minute and then subjected to a highmolding pressure for an additional two minutes. The molded samples werethen quenched in a cold (room temperature) press. 2 mm×25.4 mm diameterdisks were stamped out of the molded slabs for rheologicalcharacterization. The fluff samples were stabilized with 0.1 wt. % BHTdispersed in acetone and vacuum dried before molding. Small-strainoscillatory shear measurements were performed on an ARES rheometer(Rheometrics Inc., now TA Instruments) using parallel-plate geometry.The test chamber of the rheometer was blanketed in nitrogen in order tominimize polymer degradation. Upon sample loading and after oven thermalequilibration, the specimens were squeezed between the plates to a 1.6mm thickness and the excess was trimmed. The dynamic shear viscositieswere measured over an angular frequency range of 0.03-100 rad/s. Thesedata were fit to the Carreau-Yasuda (C-Y) equation to determinezero-shear viscosity (η₀) and other rheological parameters.

Polymerizations were performed on a 2.2 L stainless steel reactorequipped with a marine stirrer rotating at 400 rpm. The reactor wassurrounded by a stainless steel jacket through which circulated a streamof hot water that permitted precise temperature control to within half adegree centigrade. The reactor was charged with the prescribed amount ofSSA, 0.5 mL of TiBA, and a 1 mg/mL solution of catalyst in toluene, andfilled with 1.2 L of isobutane liquid, in that order, under a stream ofisobutane vapors at 45° C. Finally, ethylene was added to the reactor toequal the desired pressure, which was maintained during the experiment.In cases where comonomer was employed, 30 mL of 1-hexene were chargedinto a cylinder attached to the reactor manifold under isobutane vaporsand introduced by pressuring into the reactor with the ethylene feed.After the allotted time, the ethylene flow was stopped and the reactorwas slowly depressurized and opened to recover the granular polymerpowder. In all cases, the reactor was clean with no indication of anywall scale, coating or other forms of fouling. The polymer powder wasthen removed and weighed, and the activity was determined from thisweight and the measured time based on the amount of catalyst charged andthis data is presented in Table 1.

Example 1

A PE PARPOL of the type disclosed herein was obtained using ametallocene catalyst compound having Structure I:

The conditions used for each polymerization reaction, along with theyield and the melt index for the resulting PE polymers, designatedSamples P1-P3 and Samples 1-6, are summarized in Table 1, Table 2, andTable 3.

TABLE 1 Sample Catalyst/ m-SSA/ Ethylene/ Activity/ Density/ No. mg mgpsi T/° C. T/min Yield/g kg/g(cat)/hr g mL⁻¹ MI HLMI P1 3 72.3 420 95 50164 65.6 0.9574 >200 >500 P2 3 74.9 340 80 50 113 45.2 0.9375 >200 >500P3 3 102.2 340 80 100 172 34.4 0.9309 >200 >500

TABLE 2 MI M_(n)/1000 M_(w)/1000 Sample No. g/10 min. g/mol. g/mol.M_(w)/M_(n) P1 >200 9.2 19.7 2.2 P2 >200 8.7 20.6 2.4 P3 >200 11.3 25.12.2

TABLE 3 Reactor Ethylene Activator- Solid Sample Metallocene Time Temp.Pressure Conc. support TIBA PE MI No. [mg] [min] [° C.] [psi] [mol. %]Type [mg] [mmol] [g] g/10 min. 1 2 30 95 420 14.0 F-SSA 200 0.6 162 >2002 2 30 95 420 14.0 M-SSA 100 0.4 211 >200 3 2 30 95 420 14.0 S-SSA 1000.4 66 >200 4 2 60 95 310 5.1 M-SSA 100 0.4 28.0 143.3 5 2.6 30 90 45019.0 S-SSA 100 0.5 255 >200 6 2 30 80 340 14.4 M-SSA 100 0.4 155.0 68.4

The activator support used in conjunction with the metallocene catalystwas a chemically treated solid oxide support of the type disclosedherein where F-SSA and M-SSA designates fluoride silica-alumina solidoxide and S-SSA designates a sulfated solid oxide. Triisobutylaluminum(TIBA) was the cocatalyst in all cases. Table 2 presents the melt indexand molecular weight characteristics for samples P1-P3.

Samples 1-6 were also characterized for the presence and the type of SCBby ¹³C NMR spectroscopy. The results of these characterizations aresummarized in Table 4.

TABLE 4 Sample No. Me (wt. %) Et (wt. %) Bu (wt. %) SCB/1000 C. 1 0.031.2 0.02 3.1 2 0.03 1.2 0.02 3.1 3 0.02 1.19 0 3.1 4 0.08 1.09 0.28 3.45 0.01 1.27 0 3.2 6 0.02 1.52 0.13 4.1

The results summarized in Table 4 indicate the type of SCB did notdiffer substantially from one sample to another. The Me and Bu SCBs wereslightly elevated for Sample 4 (0.08 wt. % and 0.28 wt. %,respectively), when compared to all the other samples. Sample 6 displaysthe highest number of Et SCBs (1.52 wt. %). A comparison of the overallin situ SCB for all samples demonstrated that the level of SCB rangedfrom 3.1 to 4.1 SCB/10³ carbons, with the highest level of branchingobserved for Sample 6. The vinylidene unsaturation is fairly similar forall samples. The vinyl and trans unsaturation, as well as the totalunsaturation is presented in Table 5.

TABLE 5 Total (Vinyl + Vinylidene + Sample Vinyl/ Vinylidene/ Cis/Trans/ Trans)/ No. 1000 C. 1000 C. 1000 C. 1000 C. 1000 C. 1 1.36 0.160.00 0.34 1.86 2 1.59 0.17 0.00 0.29 2.05 3 1.09 0.13 0.00 0.29 1.51 41.55 0.11 0.00 0.59 2.25 5 0.93 0.18 0.00 0.14 1.25 6 0.79 0.23 0.000.15 1.17

A PE sample, designated Sample 7, was prepared using a chromium-basedcatalyst (0.1387 g) which was reacted with ethylene monomer at 100° C.and 300 psi for 43 minutes. Various properties of Sample 7 are presentedin Table 6.

TABLE 6 M_(n)/ Sample Catalyst Polymer MI g/ 1000 g/ M_(w)/1000 g/ No.Charge Yield [g] 10 min. mol. mol. M_(w)/M_(n) 7 0.1387 31 67.3 7.5 50.76.7

The M_(w) of Sample 7 was fairly large (50.7 kDa) when compared to theM_(w) of the metallocene-based polymers of example 1 (i.e., Samples1-6). Sample 7 also displayed a large PDI (M_(w)/M_(n) of 6.7) which wasabout three times larger than the PDIs observed for themetallocene-based polymers of example 1.

Example 2

An RCR of the type disclosed herein was prepared and the properties ofthe resin investigated. A PE PARPOL of the type described in Example 1,with a MI greater than 200 g/10 min. and a M_(w) in the range of 17-18kDa, were fed along with a coupling compound,2,5-dimethyl-2,5-di-(t-butylperoxy) hexane (DHBP), into a twin-screwmicrocompounding extruder, for example DACA's 5 cc microcompoundingextruder, or DSM-Explore's 15 cc microcompounding extruder, having adivisible extruder barrel. In all examples to follow, DHBP was thecoupling compound utilized in the preparation of the RCR unlessotherwise noted. The extrusion temperature profile was from 190° C. to215° C., and the residence time was 120 s. These temperature andresidence time conditions ensured that greater than 97% of the DHBPdecomposed while in the extruder. The resulting RCR had an MI that wasless than 2 g/10 min. and a HLMI greater than 7 g/10 min., with a M_(w)ranging from 68 to 130 kDa. High load melt index (HLMI, g/10 min) wasdetermined in accordance with ASTM D1238 condition E at 190° C. with a21,600 gram weight.

Polyethylene samples and prescribed peroxide amounts were charged into asmall container and mechanically agitated/mixed for several minutes toaffect impregnation of the peroxide. The impregnated fluff was chargedinto the microcompounding extruder, used in recirculation mode, in1.0-1.5 g portions. After the prescribed residence time was completed,the instrument was switched to continuous extrusion mode and the polymerwas extruded. The strands were collected and pelletized. Prior to samplecollections and between experiments, 3 to 10 grams of material wereextruded and used to remove any contaminants from the extruder andprevent cross-contamination between samples.

Example 3

The properties of an RCR_(homo) were investigated. Five RCR_(homo)samples, designated Samples 8-12, were prepared by reactive extrusion ofPARPOL, a PE homopolymer, in the presence of DHBP. Table 7 provides theamount of DHBP utilized to prepare each sample and various properties ofthe sample. Also presented as a comparative are the values of theseproperties for the PARPOL, designated C1, used to prepare the samples.

TABLE 7 M_(n)/ M_(w)/ MI HLMI Sample DHBP 1000 g/ 1000 g/ M_(w)/ Densityg/ g/ No. [wt. %] mol mol M_(n) g/ml 10 min. 10 min. C1 — 7.13 17.012.39 0.9574 >200 >500  8 1.04 13.43 79.59 5.93 0.9490 1.2 81.7  9 1.2014.55 75.73 5.20 0.9495 0.7 71.4 10 1.30 14.41 73.82 5.13 0.9490 0.242.2 11 1.40 13.88 70.69 5.09 0.9490 0.1 20.9 12 1.50 13.47 68.59 5.090.9473 0 14.1

The M_(n) for the RCR_(homo) samples (13-14 kDa) was independent of theamount of coupling agent used in the reactive extrusion process, and wasabout twice as large as the M_(n) of the PARPOL (7.13 kDa). The M_(w)for the RCR_(homo) samples (69-80 kDa) was also independent of theamount of the coupling agent used, and was 4-5 times larger than theM_(w) of the PARPOL, sample C1 (17.01 kDa).

The PDI (M_(w)/M_(n)) of the RCR_(homo) samples appeared to slightlydecrease with an increase in the amount of DHBP used, from a PDI of 5.93in the case of Sample 8 to a PDI of 5.09 in the case of Sample 12. Inall cases, the PDI for the RCR_(homo) samples was more than twice aslarge as the PDI for the parent homopolymer (2.39). The molecular weightdistribution profile of Samples 8-12 and C1 are plotted in FIG. 1. Theresults demonstrate the RCR_(homo) samples (i.e., samples 8-12) had alarger PDI than the parent polymer (i.e., sample C1). The change in MIfrom the PARPOL to RCR_(homo) is shown in FIG. 2.

LCB distribution profiles for RCR_(homo) samples 8-12 were determinedusing Eqs. 5 and 6 and are shown in FIG. 3. Rheology was employed forfurther study of the resins listed in FIG. 4. The relationship betweenη_(o) and M_(w) for the RCR_(homo) samples is plotted in FIG. 5. Notethat the black solid line in FIG. 6 is the 3.4-power law line. TheArnett 3.4-power law is described by equation 5:η_(o) =kM _(w) ^(3.4)  (5)

where

η_(o)=zero shear viscosity (Pa·s) [defines the Newtonian plateau]

k=Arnett law constant

M_(W)=weight average molecular weight (Da).

and represents the expected dependence of zero shear viscosity forlinear polymers when plotted against the weight average molecularweight. The RCR_(homo) samples are characterized by a rheologicalbehavior that can be described as deviating significantly from theArnett 3.4-power law FIG. 5. The melt zero-shear viscosities for theRCR_(homo) samples are several orders of magnitude greater than that ofa linear non-branched polymer of the same M_(w), which is what theArnett 3.4-power law line describes.

A statistic commonly used to quantify LCB content is α, the fraction ofthe total carbons that are long-branch vertexes. A more detaileddescription of LCBs, α, long-branch vertexes may be found in J. Janzenand R. H. Colby, J. Mol. Structure, 485-6, p. 569 (1999), which isincorporated by reference herein in its entirety. α is defined byequation 6:

$\begin{matrix}{\alpha = \frac{\upsilon_{3}}{M_{w}/M_{0}}} & (6)\end{matrix}$

where

ν₃=number of long branch vertexes

M_(W)=weight average molecular weight (Da)

M₀=molecular weight of repeating unit (Da).

For linear or mostly linear polymers, when α=0, i.e., there are no longbranch vertexes present, the Arnett 3.4-power law applies, as seen inFIG. 5. When α≠0, i.e., there are long branch vertexes present, theArnett 3.4-power law no longer applies, and there is a positivedeviation from the Arnett 3.4-power law: the higher the number of longbranch vertexes present, the higher the α value, the higher thedeviation. When an exceptionally high level of long-chain branching isreached, a negative deviation from the Arnett 3.4-power law occurs.Referring to FIG. 5, the higher the peroxide loading used in preparationof the RCR_(homo) samples, the higher the positive deviation from theArnett 3.4-power law, meaning the higher the number of long branchvertexes present.

RCR_(homo) Comparison to Commercially Available Low Density Polyethylene(LDPE) Resins

The properties of RCR_(homo) sample 8 were compared to the properties offive commercially available low density polyethylene (LDPE) resins:WESTLAKE EF378 LDPE, MARFLEX 5430 LDPE, MARFLEX 1017 LDPE, MARFLEX 4517LDPE, and MARFLEX 4751 LDPE. WESTLAKE EF378 LDPE, MARFLEX 5430 LDPE, andMARFLEX 4571 LDPE are low density polyethylene resins for cast filmapplications. MARFLEX 1017 LDPE and MARFLEX 4517 LDPE are extrusioncoating grade low density polyethylene resins. WESTLAKE EF378 LDPE issuggested for cast film applications and is available from WestlakeChemicals. MARFLEX 5430 LDPE, MARFLEX 1017 LDPE, MARFLEX 4517 LDPE, andMARFLEX 4571 LDPE are available from Chevron Phillips Chemical Company,LP.

FIG. 6 is a plot of the molecular weight distribution profiles ofRCR_(homo) Sample 8 and the five commercial LDPE resins. Dynamicrheology curves for RCR_(homo) Sample 8 and the five LDPE resins arepresented in FIG. 7. As shown in FIG. 7, the data for each of thesamples can be fitted to the C-Y equation very well. The C-Y fittingcurves are the solid lines, while the data points represent theexperimentally collected data.

FIG. 8 presents plots of the melt zero-shear viscosity as a function ofthe M_(w) for RCR_(homo) Sample 8 and the LDPE resins. Rheologicalevidence for the presence of hyperbranching in polyethylene, as is thecase for LDPE, involves the negative deviation from the Arnett 3.4-powerlaw. Such a deviation would indicate that polymer chains in the melthave extremely poor entanglement with surrounding chains due to thepresence of heavily long-chain branched material, and would result inreduced melt zero-shear viscosities. In FIG. 6, when α=0, i.e., it isexpected that there are no long branch vertexes present, and that theArnett 3.4-power law applies; two of the commercial autoclave LDPEsamples (i.e., MARFLEX 4517, MARFLEX 4571) fall on this line, despitetheir high levels of long chain branching. When α>0, i.e., there arelong branch vertexes present, the Arnett 3.4-power law no longerapplies, and there is a positive deviation from the Arnett 3.4-powerlaw: the higher the number of long branch vertexes present, the higherthe α value, the higher the deviation. This is the case for two of thecommercial LDPE samples (i.e., WESTLAKE EF378, MARFLEX 5430) and forRCR_(homo) sample 8. One of the commercial samples (i.e., MARFLEX 1017)displays the most pronounced negative deviation from the Arnett3.4-power law. For all the commercial LDPE examples, the amount of LCB,as measured by SEC-MALS is underestimated by several orders ofmagnitude. This underestimation of long chain branching in the Arnettplot is a sign of hyperbranching, where the high amounts of LCB limitchain entanglement.

Example 4

Seven RCR_(cop) samples, designated samples 13 to 19, were prepared andtheir properties investigated. The PARPOL for each sample, indicated inTable 8, was either copolymer 2 which was a copolymer of ethylene and1-hexene of 0.9375 g/mL density or copolymer 3 which was a copolymer ofethylene and 1-hexene of 0.9264 g/mL density. Copolymer 2 and copolymer3 are experimental resins produced via a slurry batch reactor asdescribed under Polymerization Reactor. Various properties of thePARPOLs and RCR_(cop) samples are also presented in Table 8.

TABLE 8 Sample Base DHBP M_(w)/M_(n) Density HLMI No. Resin [wt. %]M_(n)/1000 g/mol M_(w)/1000 g/mol g/mol g/ml MI g/10 min. g/10 min. C2 —— 7.53 18.01 2.39 0.9375 >200 >200 C3 — — 6.33 17.94 2.830.9264 >200 >200 13 C2 1.20 14.47 72.19 4.99 0.9373 1.7 56.4 14 C2 1.3015.16 75.6 4.99 0.9373 0.3 51.2 15 C2 1.40 13.56 71.7 5.29 0.9360 0.322.7 16 C2 1.60 14.29 70.56 4.94 0.9371 0 10.4 17 C2 1.70 14.92 75.635.07 0.9377 0 7.2 18 C3 2.00 11.17 69.53 6.22 0.9264 0.8 130.1 19 C32.10 — — — — 0.3 50.3

The M_(n) for the RCR_(cop) was independent of the amount of thecoupling agent used in the reactive extrusion process, and was abouttwice as large as the M_(n) for the PARPOL (6-7 kDa). The M_(w) for theRCR_(cop) samples was also independent of the amount of the couplingagent used, and it was about 4 times larger than M_(w) for the PARPOL(18 kDa). The changes in molecular weight between C2 and samples 13-17are depicted in FIG. 9.

The MI and HLMI values were high for the PARPOL (>200 g·10 min.), anddecreased for the RCR_(cop) samples. The peroxide loading during thereactive extrusion process influenced the MI and HLMI values in aninversely proportional manner, see Table 8. The higher the DHBP loading,the lower the MI and HLMI values for the RCR_(cop) samples. The changein MI and HLMI with DHBP loading for samples 13-17 are shown in FIG. 10.However, when comparing the RCR_(homo) samples of Example 3 theRCR_(cop) samples required greater amounts of peroxide to achievesimilar MI and HLMI values.

Dynamic rheology curves for RCR_(cop) Samples 13-17 are presented inFIG. 11. As shown in FIG. 11, the data for each of the samples can befitted to the C-Y equation very well. The C-Y fitting curves are thesolid lines, while the data points represent the experimentallycollected data. FIG. 12 presents plots of the melt zero-shear viscosityas a function of the M_(w) for RCR_(cop) Samples 13-17.

Example 5

The properties of four RCR_(HMW) samples of the type disclosed hereinwere investigated. The samples, designated samples 20-28, were preparedfrom a PARPOL which was a PE polymer with a molecular weight of 26,500 gmol⁻¹, designated C4. Various properties of the RCR_(HMW) are displayedin Table 9.

TABLE 9 M_(n)/ M_(w)/ MI HLMI DHBP 1000 g/ 1000 g/ M_(n)/ Density g/ g/Sample [wt. %] mol mol M_(w) g/cc 10 min. 10 min. C4 — 6.91 26.50 3.840.9737 >200 >200 20 1.40 4.39 79.50 18.11 0.9708 18.1 >200 21 1.50 5.0781.70 16.10 0.9711 16.1 >200 22 1.90 4.85 95.30 19.65 0.9715 7.3 >200 232.00 5.20 98.80 18.99 0.9715 6.3 >200 24 2.30 5.27 108.70 20.65 0.97263.8 >200 25 2.50 5.41 95.60 17.66 0.9729 2.9 >200 26 2.80 5.65 94.6016.74 0.9741 1.9 179.9 27 3.10 6.17 84.30 14.03 0.9740 0.8 121.0 28 3.406.91 81.90 13.27 0.9746 0.4 74.6

The M_(n) for the RCR_(HMW) samples (4-5 kDa) was independent of theamount of the coupling agent used in the reactive extrusion processhowever, the M_(n) was lower for the RCR_(HMW) samples than for thePARPOL, Sample C4 (7 kDa).

The M_(w) of the RCR_(HMW) samples was dependent on the amount of thecoupling agent used with the M_(w) increasing with increasing amounts ofcoupling agent (i.e., DHBP). The change in M_(w) as a result of theradical coupling process for Samples C4 and 20-23 is shown in FIG. 13.

The PDI (M_(w)/M_(n)) of the RCR_(HMW) samples were fairly independentof the amount of DHBP used. The MI and HLMI of Sample C4 was higher(>200 g/10 min.) than that of the RCR_(HMW) samples. The amount ofperoxide used influenced the MI in an inversely proportional manner, asshown in FIG. 14. The higher the DHBP loading, the lower the MI valuesfor the RCR_(HMW) samples. The curve in FIG. 14 indicates an exponentialincrease in the MI with the decrease in the amount of peroxide used.

Dynamic rheology curves for RCR_(HMW) Samples 20-28 are presented inFIG. 15. As shown in FIG. 15, the data for each of the samples can befitted to the C-Y equation very well. The C-Y fitting curves are thesolid lines, while the data points represent the experimentallycollected data. FIG. 15 presents plots of the melt zero-shear viscosityfor RCR_(HMW) Samples 20-28.

The amount of LCB, as measured by SEC-MALS, for RCR_(HMW) is shown inFIG. 16.

Comparison to Commercially Available Low Density Polyethylene (LDPE)Resins

The properties of RCR_(HMW) samples were compared to the properties ofthe LDPE resins: WESTLAKE EF378 LDPE, MARFLEX 5430 LDPE, MARFLEX 1017LDPE, MARFLEX 4517 LDPE, and MARFLEX 4751 LDPE.

The molecular weight distribution profiles of Samples 20-23 and thecommercial LDPE resins are plotted in FIG. 17. While the M_(w) issimilar for the Samples 20-23, and the LDPE samples, the MWD profile ofthe LDPE resins is broader than that of the RCR_(HMW) samples.

FIG. 18 displays dynamic rheology curves for samples 20-23 and the fiveLDPEs. As shown in FIG. 18, all polymer samples rheological behavior canbe fitted with the C-Y equation very well. The C-Y fitting curves arethe solid lines for the resin samples from Table 8 and the dashed linesfor the commercially available LDPEs, while the data points representthe experimentally collected data. Overall viscosity values arecomparable between the RCR_(HMW) samples and the LDPE resin suggestingthe resins would display similar processability.

FIG. 19 presents an Arnett plot of the melt zero-shear viscosity as afunction of the M_(w) for the RCR_(homo) Samples 20-23 and the LDPEresins. Referring to FIG. 19, when α=0, i.e., it is expected that thereare no long branch vertexes present, that the Arnett 3.4-power lawapplies; two of the commercial autoclave LDPE samples (i.e., MARFLEX4517, MARFLEX 4571) fall on this line, despite their high levels of longchain branching. When α>0, i.e., there are long branch vertexes present,the Arnett 3.4-power law no longer applies, and there is a positivedeviation from the Arnett 3.4-power law: the higher the number of longbranch vertexes present, the higher the α value, the higher thedeviation. This is the case for two of the commercial LDPE samples(i.e., WESTLAKE EF378, MARFLEX 5430) and for RCR_(HMW) Samples 20-23.One of the commercial samples (i.e., MARFLEX 1017) displays the mostpronounced negative deviation from the Arnett 3.4-power law. For Samples20-23 as well as all the commercial LDPE examples, the amount of LCB, asmeasured by SEC-MALS and ¹³C NMR spectroscopy is underestimated byseveral orders of magnitude. This underestimation of long chainbranching in the Arnett plot is a sign of hyperbranching, where the highamounts of LCB limit chain entanglement.

The effect of resin type (metallocene vs. Ziegler) on the behavior ofthe RCR_(HMW) samples was investigated. Various properties of RCR_(HMW)samples produced using metallocene-based polyethylene resins, designatedsamples 29-36, and RCR_(HMW) samples produced using Ziegler-basedpolyethylene resins, designated samples 37-44, are presented in Table 10and Table 11, respectively.

Data are also presented for the PARPOL, designated C5 in Table 10 and C6in Table 11.

TABLE 10 M_(n)/ M_(w)/ MI HLMI DHBP 1000 g/ 1000 g/ M_(w)/ Density g/ g/Sample [wt. %] mol mol M_(n) g/ml 10 min. 10 min. C5 — 6.16 30.91 5.020.9741 >200 >200 29 1.4 6.71 60.62 9.03 0.9729 38.1 >200 30 1.6 6.5966.21 10.05 0.9730 27.6 >200 31 1.9 6.33 68.64 10.84 0.9730 16.8 >200 322.3 6.85 71.78 10.48 0.9734 8.4 >200 33 2.5 6.62 70.57 10.66 0.97447.8 >200 34 2.8 6.61 70.27 10.63 0.9745 3.8 >200 35 3.1 6.53 72.94 11.170.9751 1.7 187.1 36 3.4 6.55 68.71 10.49 0.9763 1.1 143.1

TABLE 11 M_(n)/ M_(w)/ MI HLMI DHBP 1000 g/ 1000 g/ M_(w)/ Density g/ g/Sample [wt. %] mol. mol. M_(n) g/ml 10 min. 10 min. C6 — 8.16 49.27 6.040.9710 >200 >200 37 1.0 8.76 75.94 8.67 0.9670 4.2 >200 38 1.2 8.5271.25 8.36 0.9660 2.2 >200 39 1.3 8.28 71.08 8.58 0.9658 1.4 172.4 401.5 8.3 65.28 7.87 0.9672 1.6 151.2 41 1.8 7.75 63.95 8.25 0.9670 0.987.5 42 2.1 9.21 80.12 8.70 0.9677 0.4 81.7 43 2.4 8.89 80.36 9.040.9681 0.1 44.4 44 2.8 8.52 77.02 9.04 0.9689 0.0 22.1

For RCR_(HMW) samples 29-36 (i.e., metallocene resins) the M_(W) of thepolymer was found to increase with increasing concentrations of thecoupling agent, DHBP, while the remained constant when compared to thesame property for their PARPOL (i.e., Sample C5). The MI values forRCR_(HMW) samples 29-36 (i.e., metallocene resin PARPOL) were found todecrease with an increase in the amount of coupling agent used. When theamount of coupling agent used was high (>3 wt. %), the HLMI also startedto decrease with increasing the amount of DHBP. The properties of theRCR_(HMW) samples 37-44 (i.e., Ziegler resin PARPOL) were similar tothose observed for RCR_(HMW) samples 29-36.

Coagent Effect

The effect of the coagent during the reactive extrusion process on theproperties of the RCR samples was investigated. The PARPOL was the highMW PE that was also used for the data in Table 9. For reactiveextrusion, the PARPOL (C4) was contacted with the coupling agent DHBPand the coagent triallyl cyanurate (TAC) in the amounts indicated inTable 12 to produce Samples 45-52.

TABLE 12 MI HLMI Sample No. DHBP [wt. %] TAC [wt. %] g/10 min. g/10 min.45 1.40 — 18.1 >200 56 1.40 0.15 9.0 >200 57 1.40 0.30 2.7 >200 58 1.400.45 0.7 87.3 49 1.04 — 44.7 >200 50 1.04 0.15 14.5 >200 51 1.04 0.307.0 >200 52 1.04 0.45 2.6 153.3

For each of the coupling agent concentrations used, an increase in theamount of coagent led to a decrease in the MI for the RCR_(HMW). Whenthe coagent concentration reached a value of 0.45 wt. %, the HLMI forthe RCR_(HMW) samples started to decrease as well. The results in Table11 indicate that the presence of a coagent can allow for a 26% reduction(from 1.40 wt. % to 1.04 wt. %) in the amount of coupling compound whilepreserving desirable characteristics of the RCR, such as elevated HLMI.

Additional Disclosure

The following enumerated embodiments are provided as non-limitingexamples.

A first embodiment which is an ethylene polymer having a density greaterthan about 0.930 g/ml and a level of long chain branching ranging fromabout 0.001 LCB/10³ carbons to about 1.5 LCB/10³ carbons as determinedby SEC-MALS.

A second embodiment which is the polymer of the first embodiment havinga weight-average molecular weight ranging from about 25 Kg/mol to about250 Kg/mol.

A third embodiment which is the polymer of any one of the first throughsecond embodiments having a polydispersity index of from about 4 toabout 40.

A fourth embodiment which is the polymer of any one of the first throughthird embodiments having at least two types of short chain branching.

A fifth embodiment which is the polymer of the fourth embodiment whereinthe types of short chain branching are selected from the groupconsisting of ethyl, butyl, hexyl, 4-methylpentyl and octyl.

A sixth embodiment which is the polymer of any one of the first throughfifth embodiments having a flow activation energy of from about 35 kJmol⁻¹ to about 70 kJ mol⁻¹.

A seventh embodiment which is an ethylene polymer having a level ofshort chain branching ranging from about 0 to about 10 mol. % and alevel of long chain branching ranging from about 0.001 LCB/10³ carbonsto about 1.5 LCB/10³ carbons as determined by SEC-MALS.

An eighth embodiment which is an ethylene polymer having apolydispersity index ranging from about 8 to about 25 and a level oflong chain branching ranging from about 0.001 LCB/10³ carbons to about1.5 LCB/10³ carbons as determined by SEC-MALS.

A ninth embodiment which is the polymer of the eighth embodiment havinga weight-average molecular weight ranging from about 25 Kg/mol to about250 Kg/mol.

A tenth embodiment which is the polymer of any one of the eighth throughninth embodiments having a polydispersity index of from about 4 to about40.

An eleventh embodiment which is the polymer of any one of the eighththrough tenth embodiments having a weight-average molecular weightranging from about 25 Kg/mol to about 175 Kg/mol and an Eta₀ value lessthan about y where y=2E+09x²−1E+12x+6E+13 and x is the weight-averagemolecular weight.

A twelfth embodiment which is the polymer of any one of the eighththrough eleventh embodiments having a density greater than about 0.930g/ml.

A thirteenth embodiment which is the polymer of any one of the eighththrough twelfth embodiments having at least two types of short chainbranching.

A fourteenth embodiment which is the polymer of the thirteenthembodiment wherein the types of short chain branching are selected fromthe group consisting of ethyl, butyl, hexyl, 4-methylpentyl and octyl.

A fifteenth embodiment which is the polymer of any one of the eighththrough fourteenth embodiments having an activation energy of from about35 kJ mol⁻¹ to about 70 kJ mol⁻¹.

A sixteenth embodiment which is the polymer of any one of the eighththrough fifteenth embodiments having a level of short chain branchingranging from about 0 to about 10 mol. %.

A seventeenth embodiment which is an ethylene polymer having a densityless than about 0.95 g/ml; a length of short chain branching whereinless than about 10% of the short-chain branches are odd; and a level oflong chain branching ranging from about 0.001 LCB/10³ carbons to about1.5 LCB/10³ carbons as determined by SEC-MALS.

An eighteenth embodiment which is the polymer of the seventeenthembodiment having a polydispersity index of from about 4 to about 40.

A nineteenth embodiment which is the polymer of any one of theseventeenth through eighteenth embodiments wherein the types of shortchain branching are selected from the group consisting of ethyl, butyl,hexyl, 4-methylpentyl and octyl.

A twentieth embodiment which is an ethylene polymer having a level ofshort chain branching ranging from about 0 to about 10 mol. %; a lengthof short chain branching wherein less than about 10% of the short-chainbranches are odd; and a level of long chain branching ranging from about0.001 LCB/10³ carbons to about 1.5 LCB/10³ carbons as determined bySEC-MALS.

A twenty-first embodiment which is an ethylene polymer having a densityof greater than about 0.930 g/ml; an activation energy of from about 37kJ mol⁻¹ to about 55 kJ mol⁻¹; and a level of long chain branchingranging from about 0.001 LCB/10³ carbons to about 1.5 LCB/10³ carbons asdetermined by SEC-MALS.

A twenty-second embodiment which is an ethylene polymer having a levelof short chain branching ranging from about 0 to about 10 mol. %; anactivation energy of from about 37 kJ mol⁻¹ to about 55 kJ mol⁻¹; and alevel of long chain branching ranging from about 0.001 LCB/10³ carbonsto about 1.5 LCB/10³ carbons as determined by SEC-MALS.

A twenty-third embodiment which is an ethylene polymer having a densitygreater than about 0.930 g/ml; and a level of long chain branchingranging from about 0.001 LCB/10³ carbons to about 1.5 LCB/10³ carbons asdetermined by SEC-MALS wherein for a weight average molecular weightranging from about 25 kDa to about 175 kDa, a value of Eta₀ is less thany where y=2E⁰⁹x²−1E+12x+6E¹³ and x is the weight-average molecularweight.

A twenty-fourth embodiment which is an ethylene polymer having a levelof short chain branching ranging from about 0 to about 10 mol. %; and alevel of long chain branching ranging from about 0.001 LCB/10³ carbonsto about 1.5 LCB/10³ carbons as determined by SEC-MALS wherein for aweight average molecular weight ranging from about 25 kDa to about 175kDa, a value of Eta₀ is less than y where y=2E⁰⁹x²−1E+12x+6E¹³ and x isthe weight-average molecular weight.

A twenty-fifth embodiment which is the polymer of the twenty-fourthembodiment wherein less than about 10% of the short-chain branches areodd.

A twenty-sixth embodiment which is the polymer of any one of thetwenty-fourth through twenty-fifth embodiments having at least two typesof short chain branching.

A twenty-seventh embodiment which is the polymer of the twenty-sixthembodiment wherein the types of short chain branching are selected fromthe group consisting of ethyl, butyl, hexyl, 4-methylpentyl and octyl.

A twenty-eighth embodiment which is the polymer of any one of thetwenty-fourth through twenty-seventh embodiments having an activationenergy of from about 37 kJ mol⁻¹ to about 55 kJ mol⁻¹.

A twenty-ninth embodiment which is the polymer of any one of thetwenty-fourth through twenty-eighth embodiments having a polydispersityindex of from about 4 to about 40.

A thirtieth embodiment which is an ethylene polymer having a level ofshort chain branching ranging from about 0 to about 10 mol. %; and alevel of long chain branching ranging from about 0.001 LCB/10³ carbonsto about 1.5 LCB/10³ carbons as determined by SEC-MALS wherein for aweight average molecular weight ranging from about 25 kDa to about 175kDa, a value of Eta₀ is less than y where y=2E⁰⁹x²−1E+12x+6E¹³ and x isthe weight-average molecular weight.

A thirty-first embodiment which is a method comprising melt extruding awax having a weight average molecular weight ranging from about 50 kDato about 350 kDa in the presence of at least one coupling compound andan optional coagent wherein the coupling agent is a free radicalinitiator; and recovering a radically coupled resin.

While various embodiments have been shown and described, modificationsthereof can be made without departing from the spirit and teachings ofthe disclosure. The embodiments described herein are exemplary only, andare not intended to be limiting. Many variations and modifications ofthe subject matter disclosed herein are possible and are within thescope of the disclosure. Where numerical ranges or limitations areexpressly stated, such express ranges or limitations should beunderstood to include iterative ranges or limitations of like magnitudefalling within the expressly stated ranges or limitations (e.g., fromabout 1 to about 10 includes, 2, 3, 4, etc.; greater than 0.10 includes0.11, 0.12, 0.13, etc.). Use of the term “optionally” with respect toany element of a claim is intended to mean that the subject element isrequired, or alternatively, is not required. Both alternatives areintended to be within the scope of the claim. Use of broader terms suchas comprises, includes, having, etc. should be understood to providesupport for narrower terms such as consisting of, consisting essentiallyof, comprised substantially of, etc.

Accordingly, the scope of protection is not limited by the descriptionset out above but is only limited by the claims which follow, that scopeincluding all equivalents of the subject matter of the claims. Each andevery claim is incorporated into the specification as an embodiment ofthe present disclosure. Thus, the claims are a further description andare an addition to the embodiments of the present disclosure. Thediscussion of a reference in the disclosure is not an admission that itis prior art to the present disclosure, especially any reference thatmay have a publication date after the priority date of this application.The disclosures of all patents, patent applications, and publicationscited herein are hereby incorporated by reference, to the extent thatthey provide exemplary, procedural or other details supplementary tothose set forth herein.

What is claimed is:
 1. An ethylene polymer having a density greater than0.950 g/ml, a level of short chain branching ranging from 3.1 SCB/10³carbons to 3.2 SCB/10³ carbons, a level of long chain branching rangingfrom about 0.001 LCB/10³ carbons to about 1.5 LCB/10³ carbons asdetermined by SEC-MALS, and a melt index of greater than about 200 g/10min at 190° C. and 2.16 kg as determined in accordance with ASTM D1238.2. The polymer of claim 1 having a weight-average molecular weightranging from about 25 Kg/mol to about 250 Kg/mol.
 3. The polymer ofclaim 1 having a polydispersity index of from about 4 to about
 40. 4.The polymer of claim 1 having at least two types of short chainbranching.
 5. The polymer of claim 4 wherein the types of short chainbranching are selected from the group consisting of methyl, ethyl,butyl, hexyl, 4-methylpentyl and octyl.
 6. The polymer of claim 1 havinga flow activation energy of from about 35 kJ mol⁻¹ to about 70 kJ mol⁻¹.7. An ethylene polymer having a density of greater than 0.950 g/ml; alevel of short chain branching ranging from 3:1 SCB/10³ carbons to 3.2SCB/10³ carbons; a length of short chain branching wherein less thanabout 10% of the short-chain branches are odd; a level of long chainbranching ranging from about 0.001 LCB/10³ carbons to about 1.5 LCB/10³carbons as determined by SEC-MALS; a melt index of greater than about200 g/10 min at 190° C. and 216 kg as determined in accordance with ASTMD1238; and methyl, ethyl, and butyl short chain branching.